Insufficient endothelialization of cardiovascular grafts is a major hurdle in vascular surgery and regenerative medicine, bearing a risk for early graft thrombosis. Neither of the numerous strategies pursued to solve these problems were conclusive. Endothelialization is regulated by the endothelial basement membrane (EBM), a highly specialized part of the vascular extracellular matrix. Thus, a detailed understanding of the structure–function interrelations of the EBM components is fundamental for designing biomimetic materials aiming to mimic EBM functions. In this review, a detailed description of the structure and functions of the EBM are provided, including the luminal and abluminal interactions with adjacent cell types, such as vascular smooth muscle cells. Moreover, in vivo as well as in vitro strategies to build or renew EBM are summarized and critically discussed. The spectrum of methods includes vessel decellularization and implant biofunctionalization strategies as well as tissue engineering-based approaches and bioprinting. Finally, the limitations of these methods are highlighted, and future directions are suggested to help improve future design strategies for EBM-inspired materials in the cardiovascular field.